Question

1. if (mangle mkl = 83^{circ}), (mangle jkl = 127^{circ}), and (mangle jkm=(9x - 10)^{circ}), find the value of (x). g) if (mangle ebf = 117)

Explanation:

Step1: Identify angle - relationship

We know that $\angle{JKL}=\angle{JKM}+\angle{MKL}$.

Step2: Substitute the given values

Substitute $m\angle{JKL} = 127^{\circ}$, $m\angle{MKL}=83^{\circ}$ and $m\angle{JKM}=(9x - 10)^{\circ}$ into the equation: $127=(9x - 10)+83$.

Step3: Simplify the right - hand side

First, simplify the right - hand side of the equation: $(9x - 10)+83=9x+(83 - 10)=9x + 73$. So the equation becomes $127=9x + 73$.

Step4: Solve for x

Subtract 73 from both sides: $127-73=9x+73 - 73$, which gives $54 = 9x$. Then divide both sides by 9: $\frac{54}{9}=x$. So $x = 6$.

Answer:

$x = 6$